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#include<cstdio>
#include<iostream>
#include<algorithm>
#include<string>
#include<vector>
#include<cmath>
#include<queue>
#include<queue>
#include<stack>
#include<bits/stdc++.h>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

typedef vector<int> VI;
typedef vector<VI> VVI;
typedef long long LL;
typedef unsigned long long ULL;
typedef long double LD;
typedef pair<int, int> PII;
typedef pair<LL, LL> PLL;
typedef vector<LL> VLL;
typedef vector<LD> VLD;
typedef vector<VLL > VVLL;
typedef vector<VLD > VVLD;
typedef vector<PII > VPII;
typedef __int128 int128;
template<class TIn>
using indexed_set = tree<
        TIn, null_type, less<TIn>,
        rb_tree_tag, tree_order_statistics_node_update>;
template<class T> using min_heap = priority_queue<T, vector<T>, greater<T>>;

#define FOR(x, b, e) for(int x=b; x<=(e); ++x)
#define FORD(x, b, e) for(int x=b; x>=(e); --x)
#define REP(x, n) for(int x=0; x<(n); ++x)
#define VAR(v, n) __typeof(n) v = (n)
#define ALL(c) (c).begin(), (c).end()
#define SIZE(x) ((int)(x).size())
#define FOREACH(i, c) for(VAR(i, (c).begin()); i != (c).end(); ++i)
#define PB push_back
#define ST first
#define ND second
#define THIS (*this)
#define LSB(x) (x & -x)
#define SQR(x) ((x)*(x))

const int INF = 1e9;

struct E {
    int v, w;
    E(int weight = 0): w(weight) {}
};
struct V: public vector<E> {};

struct Graph: public vector<V> {
    Graph(int size = 0): vector<V>(size) {}

    void addEdge(int u, int v, E e = E()) {
        addDirectedEdge(u, v, e);
        addDirectedEdge(v, u, e);
    }
    void addDirectedEdge(int u, int v, E e = E()) {
        e.v = v;
        THIS[u].PB(e);
    }
    Graph reversed() {
        Graph res(size());
        REP(u, size()) for(auto &e : THIS[u]) res.addDirectedEdge(e.v, u, e);
        return res;
    }
};

class FloydWarshall : public VVI {
    private:
    Graph &g;

    public:
    FloydWarshall(Graph &graph): g(graph) {
        assign(g.size(), VI(g.size(), INF));
        REP(i, g.size()) for (auto &e : g[i]) THIS[i][e.v] = e.w, THIS[i][i] = 0;
        REP(k, g.size()) REP(i, g.size()) REP(j, g.size()) if (THIS[i][k] < INF && THIS[k][j] < INF)
            THIS[i][j] = min(THIS[i][j], THIS[i][k] + THIS[k][j]);
    }
    bool hasNegativeCycle() { REP(i, g.size()) if (THIS[i][i] < 0) return true; return false; }
};

bool possible(int x, Graph &g, FloydWarshall &fw, int maxLen) {
    VPII longPahts;
    REP(u, g.size()) REP(v, u) {
        if (fw[u][v] > x) longPahts.PB({u, v});
    }
    REP(u, g.size()) {
        REP(v, u) if (fw[u][v] >= maxLen - x) {
            bool ok = true;
            for (auto &lp : longPahts) {
                int d = min(fw[lp.ST][u] + fw[v][lp.ND], fw[lp.ND][u] + fw[v][lp.ST]);
                if (d > x) { ok = false; break; }
            }
            if (ok) return true;
        }
    }
    return false;
}

int main() {
	ios_base::sync_with_stdio(0);
    cin.tie(NULL); cout.tie(NULL);
    int t; cin >> t;
    while (t--) {
        int n; cin >> n;
        Graph g(n);
        REP(i, n) {
            string am; cin >> am;
            REP(j, i) if (am[j] == '1') g.addEdge(i, j, E(1));
        }
        FloydWarshall fw(g);
        int l = 0, h = 0;
        REP(i, n) REP(j, i) h = max(h, fw[i][j]);
        int maxLen = h;
        while (l + 1 < h) {
            int mid = (l + h) / 2;
            if (possible(mid, g, fw, maxLen)) h = mid;
            else l = mid;
        }
        cout << h << '\n';
        fw.clear();
        g.clear();
    }

    return 0;
}